/// <summary>
/// Generate counter example for reachability and deadlock
/// [ REFS: '', DEREFS: automataBDD.transitionBDD, automataBDD.priorityTransitionsBDD, this.traces ]
/// </summary>
/// <param name="automataBDD"></param>
/// <param name="encoder"></param>
/// <returns></returns>
public void GetMCResult(AutomataBDD automataBDD, BDDEncoder encoder)
{
VerificationOutput.CounterExampleTrace.Add(InitialStep);
if (this.traces.Count > 0)
{
ExpressionBDDEncoding initEncoding = automataBDD.initExpression.TranslateBoolExpToBDD(encoder.model);
this.traces.Insert(0, CUDD.Function.Or(initEncoding.GuardDDs));
Valuation currentValuation = this.InitialStep.GlobalEnv;
Valuation lastValuation;
List <CUDDNode> allTransitions = new List <CUDDNode>();
allTransitions.AddRange(automataBDD.transitionBDD);
allTransitions.AddRange(automataBDD.Ticks);
for (int i = 1; i < this.traces.Count; i++)
{
//Get event information
CUDD.Ref(allTransitions);
CUDD.Ref(this.traces[i], this.traces[i - 1]);
CUDDNode transitionTemp = CUDD.Function.And(this.traces[i - 1], encoder.model.SwapRowColVars(this.traces[i]));
CUDDNode transWithEventInfo = CUDD.Function.And(transitionTemp, allTransitions);
transWithEventInfo = CUDD.Abstract.ThereExists(transWithEventInfo, encoder.model.AllRowVarsExceptSingleCopy);
transWithEventInfo = CUDD.RestrictToFirst(transWithEventInfo, encoder.model.AllColVars);
lastValuation = currentValuation;
currentValuation = encoder.GetValuationFromBDD(transWithEventInfo, this.InitialStep.GlobalEnv);
string eventName = encoder.GetEventChannelName(lastValuation, currentValuation, transWithEventInfo);
VerificationOutput.CounterExampleTrace.Add(new ConfigurationBDD(eventName, currentValuation));
//
CUDD.Deref(transWithEventInfo);
}
}
//
CUDD.Deref(automataBDD.transitionBDD, automataBDD.Ticks, traces);
//
VerificationOutput.ActualMemoryUsage = CUDD.ReadMemoryInUse();
VerificationOutput.numberOfBoolVars = encoder.model.NumberOfBoolVars;
encoder.model.Close();
}
/// <summary>
/// Return a computation of a buchi automata in form "prefix (period)*"
/// [ REFS: 'prefix, period', DEREFS:]
/// </summary>
/// <param name="automataBDD"></param>
/// <param name="model"></param>
public void MC(AutomataBDD automataBDD, Model model)
{
//Clear the old data
this.transitionsNoEvents.Clear();
this.prefix.Clear();
this.period.Clear();
ExpressionBDDEncoding initEncoding = automataBDD.initExpression.TranslateBoolExpToBDD(model);
if (initEncoding.GuardDDs.Count == 0)
{
return;
}
ExpressionBDDEncoding finalStateEncoding = automataBDD.acceptanceExpression.TranslateBoolExpToBDD(model);
if (finalStateEncoding.GuardDDs.Count == 0)
{
return;
}
CUDDNode initState = CUDD.Function.Or(initEncoding.GuardDDs);
CUDDNode finalState = CUDD.Function.Or(finalStateEncoding.GuardDDs);
CUDDNode finalStateWithNoEvent = CUDD.Abstract.ThereExists(finalState, model.GetAllEventVars());
CUDD.Ref(automataBDD.transitionBDD);
this.transitionsNoEvents = CUDD.Abstract.ThereExists(automataBDD.transitionBDD, model.GetAllEventVars());
CUDDNode allSCCs = SCCHull(model, initState, finalStateWithNoEvent);
if (!allSCCs.Equals(CUDD.ZERO) && VerificationOutput.GenerateCounterExample)
{
this.VerificationOutput.VerificationResult = VerificationResultType.INVALID;
//Transitions out from allSCCs
CUDD.Ref(transitionsNoEvents);
CUDD.Ref(allSCCs);
List <CUDDNode> R = CUDD.Function.And(transitionsNoEvents, allSCCs);
//pick one state from the set final
CUDD.Ref(allSCCs);
CUDDNode s = CUDD.RestrictToFirst(allSCCs, model.AllRowVars);
//while the states from which we can reach s are not all states that can be reached from s
CUDDNode scc;
while (true)
{
CUDD.Ref(s);
CUDDNode backwardOfS = model.PredecessorsStart(s, R);
CUDD.Ref(s);
CUDDNode forwardOfS = model.SuccessorsStart(s, R);
//
CUDD.Ref(backwardOfS, forwardOfS);
CUDDNode temp = CUDD.Function.Different(backwardOfS, forwardOfS);
if (temp.Equals(CUDD.ZERO))
{
scc = backwardOfS;
CUDD.Deref(forwardOfS, temp);
break;
}
else
{
CUDD.Deref(backwardOfS, forwardOfS, s);
s = CUDD.RestrictToFirst(temp, model.AllRowVars);
}
}
//R now contains only transitions within the SCC scc
CUDD.Ref(scc, scc, scc, scc);
R[0] = CUDD.Function.And(CUDD.Function.And(R[0], scc), model.SwapRowColVars(scc));
R[1] = CUDD.Function.And(CUDD.Function.And(R[1], scc), model.SwapRowColVars(scc));
CUDD.Ref(scc);
CUDDNode notInSCC = CUDD.Function.Not(scc);
List <CUDDNode> transitionNotInSCC = new List <CUDDNode>();
CUDD.Ref(transitionsNoEvents, transitionsNoEvents);
CUDD.Ref(notInSCC, notInSCC);
transitionNotInSCC.AddRange(CUDD.Function.And(transitionsNoEvents, notInSCC));
transitionNotInSCC.AddRange(CUDD.Function.And(transitionsNoEvents, model.SwapRowColVars(notInSCC)));
//prefix is now a shortest path from an initial state to a state in final
model.Path(initState, scc, transitionNotInSCC, prefix, true);
CUDD.Deref(transitionNotInSCC[0], transitionNotInSCC[1]);
//Dummy value
period.Add((prefix.Count == 0) ? initState : prefix[prefix.Count - 1]);
//cycle must pass final state
CUDD.Ref(period);
CUDD.Ref(finalStateWithNoEvent);
CUDDNode temp1 = CUDD.Function.And(CUDD.Function.Or(period), finalStateWithNoEvent);
if (temp1.Equals(CUDD.ZERO))
{
CUDD.Ref(scc, finalStateWithNoEvent);
CUDDNode acceptanceStateInCyle = CUDD.Function.And(scc, finalStateWithNoEvent);
model.Path(period[period.Count - 1], acceptanceStateInCyle, R, period, true);
CUDD.Deref(acceptanceStateInCyle);
}
CUDD.Deref(temp1);
//
bool isEmptyPathAllowed = period.Count != 1;
model.Path(period[period.Count - 1], period[0], R, period, isEmptyPathAllowed);
//Remove dummy
CUDD.Deref(period[0]); period.RemoveAt(0);
//
CUDD.Deref(initState, finalStateWithNoEvent, allSCCs, s, scc, notInSCC);
CUDD.Deref(transitionsNoEvents[0], transitionsNoEvents[1]);
CUDD.Deref(R[0], R[1]);
}
else
{
this.VerificationOutput.VerificationResult = VerificationResultType.VALID;
CUDD.Deref(initState, finalStateWithNoEvent, allSCCs);
CUDD.Deref(transitionsNoEvents[0], transitionsNoEvents[1]);
}
}
/// <summary>
/// Return the path from source to destination. If reachable, return true and path contains the path from source to destination
/// [ REFS: '', DEREFS:]
/// </summary>
/// <param name="source"></param>
/// <param name="destination"></param>
/// <param name="transitions"></param>
/// <param name="model"></param>
/// <param name="path">not include the init state</param>
/// <param name="isEmptyPathAllowed">if false, then the path must be not empty though the source satisfies the destination</param>
/// <returns></returns>
public bool PathBackWard(CUDDNode source, CUDDNode destination, List <CUDDNode> transitions, List <CUDDNode> path, bool isEmptyPathAllowed)
{
if (isEmptyPathAllowed)
{
//
CUDD.Ref(source, destination);
CUDDNode temp = CUDD.Function.And(source, destination);
//In case source already satisfies destination
if (!temp.Equals(CUDD.ZERO))
{
CUDD.Deref(temp);
return(true);
}
}
//
bool reachable = false;
List <CUDDNode> backtrackingReachability = new List <CUDDNode>();
CUDDNode allReachabeToGoal, currentReachableToGoal;
CUDD.Ref(destination, destination);
allReachabeToGoal = currentReachableToGoal = destination;
int numberOfLoop = 0;
CUDDNode commonNode = CUDD.Constant(0);
do
{
//backward
numberOfLoop++;
Debug.Write(numberOfLoop + " ");
//to find source state, now the currentReachableToGoal must be in column form (target state)
currentReachableToGoal = this.SwapRowColVars(currentReachableToGoal);
CUDD.Ref(transitions);
currentReachableToGoal = CUDD.Function.And(currentReachableToGoal, transitions);
CUDD.Ref(currentReachableToGoal);
backtrackingReachability.Add(currentReachableToGoal);
//get source state, but in row-form
currentReachableToGoal = CUDD.Abstract.ThereExists(currentReachableToGoal, AllColVars);
//Check 2 directions have intersection
CUDD.Ref(currentReachableToGoal, source);
CUDD.Deref(commonNode);
commonNode = CUDD.Function.And(currentReachableToGoal, source);
if (!commonNode.Equals(CUDD.ZERO))
{
reachable = true;
break;
}
//find fixpoint
CUDD.Ref(currentReachableToGoal, allReachabeToGoal);
CUDDNode allReachabeToGoalTemp = CUDD.Function.Or(allReachabeToGoal, currentReachableToGoal);
if (allReachabeToGoalTemp.Equals(allReachabeToGoal))
{
reachable = false;
CUDD.Deref(allReachabeToGoalTemp);
break;
}
else
{
currentReachableToGoal = CUDD.Function.Different(currentReachableToGoal, allReachabeToGoal);
allReachabeToGoal = allReachabeToGoalTemp;
}
} while (true);
Debug.WriteLine("\nPath Backward: " + numberOfLoop + " loops.");
if (!reachable)
{
CUDD.Deref(currentReachableToGoal, allReachabeToGoal, commonNode);
CUDD.Deref(backtrackingReachability);
//
backtrackingReachability.Clear();
}
else
{
//
CUDD.Deref(currentReachableToGoal, allReachabeToGoal, commonNode);
//backtrackingReachability contains transitions from source to destination
if (backtrackingReachability.Count > 0)
{
CUDDNode currentStateDD = source;
CUDD.Ref(currentStateDD);
for (int i = backtrackingReachability.Count - 1; i >= 0; i--)
{
//find the intersection
currentStateDD = CUDD.Function.And(backtrackingReachability[i], currentStateDD);
//remove all boolean variables in the row-form, it is now set of all reachable backward state
currentStateDD = CUDD.Abstract.ThereExists(currentStateDD, AllRowVars);
currentStateDD = CUDD.RestrictToFirst(currentStateDD, this.AllColVars);
currentStateDD = CUDD.Abstract.ThereExists(currentStateDD, this.GetAllEventVars());
//swap to row-variable form
currentStateDD = this.SwapRowColVars(currentStateDD);
CUDD.Ref(currentStateDD);
path.Add(currentStateDD);
}
//
CUDD.Deref(currentStateDD);
}
}
//
return(reachable);
}
/// <summary>
/// Return the path from source to destination. If reachable, return true and path contains the path from source to destination
/// [ REFS: '', DEREFS:]
/// </summary>
/// <param name="source"></param>
/// <param name="destination"></param>
/// <param name="transitions"></param>
/// <param name="model"></param>
/// <param name="path">not include the init state</param>
/// <param name="isEmptyPathAllowed">if false, then the path must be not empty though the source satisfies the destination</param>
/// <returns></returns>
public bool PathForward(CUDDNode source, CUDDNode destination, List <CUDDNode> transitions, List <CUDDNode> path, bool isEmptyPathAllowed)
{
if (isEmptyPathAllowed)
{
CUDD.Ref(source, destination);
CUDDNode temp = CUDD.Function.And(source, destination);
//In case source already satisfies destination
if (!temp.Equals(CUDD.ZERO))
{
CUDD.Deref(temp);
return(true);
}
}
//
bool reachable = false;
List <CUDDNode> forwardReachability = new List <CUDDNode>();
CUDDNode allReachableFromInit, currentReachableFromInit;
CUDD.Ref(source, source);
allReachableFromInit = currentReachableFromInit = source;
int numberOfLoop = 0;
CUDDNode commonNode = CUDD.Constant(0);
do
{
//forward
numberOfLoop++;
Debug.Write(numberOfLoop + " ");
CUDD.Ref(transitions);
currentReachableFromInit = CUDD.Function.And(currentReachableFromInit, transitions);
//Must reference because current value of currentReachableDD belonging to backtrackingReachability
CUDD.Ref(currentReachableFromInit);
forwardReachability.Add(currentReachableFromInit);
currentReachableFromInit = this.SwapRowColVars(currentReachableFromInit);
//get target state, in row-form
currentReachableFromInit = CUDD.Abstract.ThereExists(currentReachableFromInit, AllColVars);
//Check 2 directions have intersection
CUDD.Ref(destination, currentReachableFromInit);
CUDD.Deref(commonNode);
commonNode = CUDD.Function.And(destination, currentReachableFromInit);
if (!commonNode.Equals(CUDD.ZERO))
{
reachable = true;
break;
}
//find fixpoint
CUDD.Ref(currentReachableFromInit, allReachableFromInit);
CUDDNode allReachabeFromInitTemp = CUDD.Function.Or(currentReachableFromInit, allReachableFromInit);
if (allReachabeFromInitTemp.Equals(allReachableFromInit))
{
//reachable = false;
CUDD.Deref(allReachabeFromInitTemp);
break;
}
else
{
currentReachableFromInit = CUDD.Function.Different(currentReachableFromInit, allReachableFromInit);
allReachableFromInit = allReachabeFromInitTemp;
}
} while (true);
Debug.WriteLine("\nPath Forward: " + numberOfLoop + " loops.");
if (!reachable)
{
CUDD.Deref(currentReachableFromInit, allReachableFromInit, commonNode);
CUDD.Deref(forwardReachability);
//
forwardReachability.Clear();
}
else
{
//
CUDD.Deref(currentReachableFromInit, allReachableFromInit);
//in column form
commonNode = this.SwapRowColVars(commonNode);
for (int i = forwardReachability.Count - 1; i >= 0; i--)
{
forwardReachability[i] = CUDD.Function.And(forwardReachability[i], commonNode);
//in column form
CUDD.Ref(forwardReachability[i]);
commonNode = CUDD.Abstract.ThereExists(forwardReachability[i], AllColVars);
commonNode = this.SwapRowColVars(commonNode);
}
CUDD.Deref(commonNode);
//backtrackingReachability contains transitions from source to destination
if (forwardReachability.Count > 0)
{
CUDDNode currentStateDD = source;
CUDD.Ref(currentStateDD);
for (int i = 0; i < forwardReachability.Count; i++)
{
//find the intersection
currentStateDD = CUDD.Function.And(forwardReachability[i], currentStateDD);
//remove all boolean variables in the row-form, it is now set of all reachable backward state
currentStateDD = CUDD.Abstract.ThereExists(currentStateDD, AllRowVars);
currentStateDD = CUDD.RestrictToFirst(currentStateDD, this.AllColVars);
currentStateDD = CUDD.Abstract.ThereExists(currentStateDD, this.GetAllEventVars());
//swap to row-variable form
currentStateDD = this.SwapRowColVars(currentStateDD);
CUDD.Ref(currentStateDD);
path.Add(currentStateDD);
}
//
CUDD.Deref(currentStateDD);
}
}
//
return(reachable);
}
/// <summary>
/// Return the path from source to destination.
/// If reachable, return true and path contains the path from source to destination
/// Serach from two direction: forward and backward
/// [ REFS: '', DEREFS:]
/// </summary>
/// <param name="source"></param>
/// <param name="destination"></param>
/// <param name="transitions">transitions[0]: normal transitions, transitions[1]: priority transition</param>
/// <param name="model"></param>
/// <param name="path">not include the init state</param>
/// <param name="isEmptyPathAllowed">if false, then the path must be not empty though the source satisfies the destination</param>
/// <returns></returns>
public bool Path(CUDDNode source, CUDDNode destination, List <List <CUDDNode> > transitions, List <CUDDNode> path, bool isEmptyPathAllowed)
{
if (isEmptyPathAllowed)
{
CUDD.Ref(source, destination);
CUDDNode temp = CUDD.Function.And(source, destination);
//In case source already satisfies destination
if (!temp.Equals(CUDD.ZERO))
{
CUDD.Deref(temp);
return(true);
}
}
//
bool reachable = false;
List <CUDDNode> backtrackingReachability = new List <CUDDNode>();
List <CUDDNode> forwardReachability = new List <CUDDNode>();
CUDDNode allReachabeToGoal, currentReachableToGoal;
CUDD.Ref(destination, destination);
allReachabeToGoal = currentReachableToGoal = destination;
CUDDNode allReachableFromInit, currentReachableFromInit;
CUDD.Ref(source, source);
allReachableFromInit = currentReachableFromInit = source;
int nextStep = 0;
int forwardStep = 0;
int numberOfForwardNodes = 0;
int backwardSteps = 0;
int numberOfBackwardNodes = 0;
CUDDNode commonNode = CUDD.Constant(0);
do
{
if (nextStep != GoForward)
{
//backward
Debug.WriteLine("Backward: " + numberOfBDDOperation);
numberOfBDDOperation++;
//to find source state, now the currentReachableToGoal must be in column form (target state)
currentReachableToGoal = this.SwapRowColVars(currentReachableToGoal);
currentReachableToGoal = TransitionsByTargetStates(currentReachableToGoal, transitions);
CUDD.Ref(currentReachableToGoal);
backtrackingReachability.Add(currentReachableToGoal);
//get source state, but in row-form
currentReachableToGoal = CUDD.Abstract.ThereExists(currentReachableToGoal, AllColVars);
//Check 2 directions have intersection
CUDD.Ref(currentReachableToGoal, currentReachableFromInit);
CUDD.Deref(commonNode);
commonNode = CUDD.Function.And(currentReachableToGoal, currentReachableFromInit);
if (!commonNode.Equals(CUDD.ZERO))
{
reachable = true;
break;
}
//find fixpoint
CUDD.Ref(currentReachableToGoal, allReachabeToGoal);
CUDDNode allReachabeToGoalTemp = CUDD.Function.Or(allReachabeToGoal, currentReachableToGoal);
backwardSteps++;
numberOfBackwardNodes = CUDD.GetNumNodes(allReachabeToGoalTemp);
if (allReachabeToGoalTemp.Equals(allReachabeToGoal))
{
reachable = false;
CUDD.Deref(allReachabeToGoalTemp);
break;
}
else
{
currentReachableToGoal = CUDD.Function.Different(currentReachableToGoal, allReachabeToGoal);
allReachabeToGoal = allReachabeToGoalTemp;
}
}
if (nextStep != GoBackward)
{
//forward
Debug.WriteLine("Forward: " + numberOfBDDOperation);
numberOfBDDOperation++;
currentReachableFromInit = TransitionsBySourceStates(currentReachableFromInit, transitions);
//Must reference because current value of currentReachableDD belonging to backtrackingReachability
CUDD.Ref(currentReachableFromInit);
forwardReachability.Add(currentReachableFromInit);
currentReachableFromInit = this.SwapRowColVars(currentReachableFromInit);
//get target state, in row-form
currentReachableFromInit = CUDD.Abstract.ThereExists(currentReachableFromInit, AllColVars);
//Check 2 directions have intersection
CUDD.Ref(currentReachableToGoal, currentReachableFromInit);
CUDD.Deref(commonNode);
commonNode = CUDD.Function.And(currentReachableToGoal, currentReachableFromInit);
if (!commonNode.Equals(CUDD.ZERO))
{
reachable = true;
break;
}
//find fixpoint
CUDD.Ref(currentReachableFromInit, allReachableFromInit);
CUDDNode allReachabeFromInitTemp = CUDD.Function.Or(currentReachableFromInit, allReachableFromInit);
forwardStep++;
numberOfForwardNodes = CUDD.GetNumNodes(allReachabeFromInitTemp);
if (allReachabeFromInitTemp.Equals(allReachableFromInit))
{
reachable = false;
CUDD.Deref(allReachabeFromInitTemp);
break;
}
else
{
currentReachableFromInit = CUDD.Function.Different(currentReachableFromInit, allReachableFromInit);
allReachableFromInit = allReachabeFromInitTemp;
}
}
nextStep = GetNextStep(forwardStep, numberOfForwardNodes, backwardSteps, numberOfBackwardNodes);
} while (true);
if (!reachable)
{
CUDD.Deref(currentReachableToGoal, allReachabeToGoal, currentReachableFromInit, allReachableFromInit, commonNode);
CUDD.Deref(backtrackingReachability);
CUDD.Deref(forwardReachability);
//
backtrackingReachability.Clear();
forwardReachability.Clear();
}
else
{
//
CUDD.Deref(currentReachableToGoal, allReachabeToGoal, currentReachableFromInit, allReachableFromInit);
//in column form
commonNode = this.SwapRowColVars(commonNode);
for (int i = forwardReachability.Count - 1; i >= 0; i--)
{
//Kill commonNode
CUDDNode correctTransition = CUDD.Function.And(forwardReachability[i], commonNode);
CUDD.Ref(correctTransition);
backtrackingReachability.Add(correctTransition);
//in column form
commonNode = CUDD.Abstract.ThereExists(correctTransition, AllColVars);
commonNode = this.SwapRowColVars(commonNode);
}
CUDD.Deref(commonNode);
//backtrackingReachability contains transitions from source to destination
if (backtrackingReachability.Count > 0)
{
CUDDNode currentStateDD = source;
CUDD.Ref(currentStateDD);
for (int i = backtrackingReachability.Count - 1; i >= 0; i--)
{
//find the intersection
currentStateDD = CUDD.Function.And(backtrackingReachability[i], currentStateDD);
//remove all boolean variables in the row-form, it is now set of all reachable backward state
currentStateDD = CUDD.Abstract.ThereExists(currentStateDD, AllRowVars);
currentStateDD = CUDD.RestrictToFirst(currentStateDD, this.AllColVars);
currentStateDD = CUDD.Abstract.ThereExists(currentStateDD, this.GetAllEventVars());
//swap to row-variable form
currentStateDD = this.SwapRowColVars(currentStateDD);
CUDD.Ref(currentStateDD);
path.Add(currentStateDD);
}
//
CUDD.Deref(currentStateDD);
}
}
//
return(reachable);
}
